The present invention relates generally to radio frequency antenna arrays and in particular to an improved omnidirectional array utilizing a Mobius topology of R-2R lenses. Many approaches have been used for constructing wide-angle radio frequency antennas having multiple simultaneous beams. These approaches include the Luneburg lens, in which a dielectric medium with a graded dielectric constant is used to focus an incident plane wave, arriving at one side of the lens structure, to a point focus on the other side of the lens structure. The dielectric lens may have the shape of a full sphere, or a hemisphere over a conducting ground plane. Alternatively, the graded dielectric may be confined between parallel conducting surfaces, and in this case the focusing is two-dimensional rather than three-dimensional. A geodesic version of the Luneburg lens has also been described in the literature. For the geodesic version, focusing is two-dimensional, but this focusing results not from a graded dielectric constant but from the shaping of a pair of parallel conducting surfaces to make the propagating rays in the space between the surfaces come to the same kind of focus that would result from the use of a graded dielectric constant between flat conducting surfaces.
The R-KR lens is another lens design that has been used for the generation of multiple simultaneous beams from a curved aperture. In this design there is a one-to-one mapping from the array elements to the lens periphery, so that a complete circle of array elements can be mapped directly onto a single circuit of the periphery of a circular lens. However, with an R-KR lens the lens geometry does not ordinarily provide precise focusing. The resulting phase errors can lead to antenna sidelobes whose magnitude may be unacceptable high, for certain applications.
For perfect focusing, the signal received at each array element, from a distant source or radar target, will enter the lens, cross the lens to the focal point, and arrive in exact phase with the signals received at all of the other array elements that participate in the beam directed at that source or target. Imperfect focusing results when there are phase errors that keep the different signal rays from arriving in phase with each other. Phase errors that arise out of the lens geometry are collectively denoted by the term "coma aberration". The phase errors comprising the coma aberration will ordinarily vary slowly from one array element to the next, so that these errors can be expressed as a smooth function of a variable locating the elements on the circular or cylindrical array. In particular, the coma aberration can be written as a power series, a polynomial function of the angular variable A, where this angle locates a radiating element on the curved aperture. If this angle is measured from the boresight direction (the direction toward which this antenna beam is focused), then symmetry ensures that the polynomial will contain only even powers of the angle A. The R-KR lens is designed to be corrected through the squared term in this polynomial, but not through the higher terms (fourth and sixth powers, etc.).
The R-2R lens, on the other hand, provides exact phase correction, through all terms in the error polynomial. When a plane wave is incident on array elements 4 arranged on a circular arc, as shown in FIG. 1, the extra propagation distance for a ray that reaches an element at the angle A, as compared with the central ray (A=0), is given by: EQU f(A)=2R[1 -cos A](1)
where 2R is defined as the radius of the circular arc. These array elements are connected (by equal line lengths 6) to lens couplers 8 on the periphery of a parallel-plate lens 10 whose radius is R, half the radius of the antenna array. Furthermore, the element at the angle A is connected to a coupler whose angular position on the lens is 2A, as shown in FIG. 1. It can be seen that the propagation distance across the lens is equal to: EQU g(A)=2R cos A (2)
where this propagation is along a chord 12 to the focal point at the left-hand edge of the lens.
When the two segments of the propagation path are added together, the result is: EQU f(A)+g(A)=2R (3)
which is a constant, independent of the angle A which specifies the ray that is being considered. Thus all of the rays in the incident plane wave, within the region intercepted by the cylindrical antenna, will come to a common focus at the edge of the lens.
This precise focusing, together with the intrinsic simplicity of the R-2R lens, has made this lens design an attractive choice, when coverage of only a limited angular sector is desired. As is evident from FIG. 1, when an attempt is made to enlarge the cylindrical arc to 180 degrees or beyond, the doubled angle at the lens periphery extends to 360 degrees and beyond, which is not feasible with the simple arrangement of FIG. 1, since there are only 360 degrees in a full circle and once this amount of lens periphery has been utilized there is no more remaining. Even the approach toward 180 degrees of cylindrical arc (resulting in an approach toward 360 degrees of utilized lens periphery) has the effect of narrowing the portion of the lens periphery available for separate beam ports.
The allocation of a particular coupling structure to be either a beam port or an element port has this effect: as the portion of the lens periphery connected to array elements is increased, the portion available for beam ports is reduced. This limitation can be avoided, if desired, through the use of circulators, circuit elements which separate out the signals passing in opposite directions along a transmission line. The use of circulators will make possible the employment of the same coupling structures for both beam ports and element ports. However, circulators are nonreciprocal structures, and when nonreciprocal components such as circulators are used in the design of a lens antenna, it is ordinarily not possible to use the same lens antenna for both transmission and reception. This is a limitation which could be important in certain applications of multibeam antennas, particularly in the use of these antennas at nodes of survivable communications networks.